Thermal Friction Enhancement in Zwitterionic Monolayers

We introduce a model for zwitterionic monolayers and investigate its tribological response to changes in applied load, sliding velocity, and temperature by means of molecular-dynamics simulations. The proposed model exhibits different regimes of motion depending on temperature and sliding velocity. We find a remarkable increase of friction with temperature, which we attribute to the formation and rupture of transient bonds between individual molecules of opposite sliding layers, triggered by the out-of-plane thermal fluctuations of the molecules’ orientations. To highlight the effect of the molecular charges, we compare these results with analogous simulations for the charge-free system. These findings are expected to be relevant to nanoscale rheology and tribology experiments of locally-charged lubricated systems such as, e.g., experiments performed on zwitterionic monolayers, phospholipid micelles, or confined polymeric brushes in a surface force apparatus.

We need a common periodicity and therefore, a matching lattice vector with integers m 1 and m 2 . This evaluation of this common lattice vector is a special case of the theory described in Ref. 1.
Alternatively, the opposite corner (l x , l y ) of a rectangular supercell with a corner at the origin (0, 0) is obtained as (l x , l y ) = 4a 1 + 18a 2 .

Cutoff of the Two-Body Potential
For the non-bonded pairwise particle-particle interactions we adopt a Morse potential with a standard shift and a linear term added as follows: so that the truncated potential vanishes smoothly at R c .

Long-Range Solver for Coulomb Interactions
The PPPM solver used for systems, such as ours, which are periodic in x and y, but not in z, requires an ad-hoc extension. The system is treated as if it was periodic in z, but inserting an empty volume between the slabs and thus removing unphysical dipole interslab interactions. For the parameter setting the fraction of empty volume in between slab repetitions, we adopt the value 3.0 recommended by the developers of the simulation software LAMMPS. 2 We explicitly verified that, by improving the accuracy of the PPPM solver beyond 10 −4 eV/nm, neither quantitative effects on the sliding friction nor qualitative effects on the system dynamics are detectable.

S4
The Hooking Fraction h In order to quantify the degree of interpenetration of the chains we introduce a "hooking fraction" h as the fractional number of chains whose cation crosses the average level of cations of the opposite layer, like the highlighted chains in Fig. 4b,d of the main text. The definition for h is the following: where Here θ() is the usual θ function, equal to one or zero according to the sign of its argument, For example, the hooking fraction as a function of time is illustrated in Fig. 5a. h clearly correlates with the stick-slip dynamics. b charge-free Figure S6: Scatter plot illustrating the correlation between the total potential energy and the hooked fraction for (a) zwitterionic system (b) charge-free system. Correlation coefficients for these data are reported in Figure 8b of the paper. L = 10 MPa and T = 300 K.

SI Movies
Each of the SI movies reports the final 6 ns (i.e. the last 30 nm displacement) of a MD simulation. In simulation time, the frame rate is 1 frame every 20 ps. In running time, the frame rate is 10 frames per second. For clarity, like in Fig. 3 of the main text, the movies only include a 5 nm y-thick slice of the simulation cell (whose entire y-side is 14.41 nm).
Each movie contains one highlighted SUP particle to make the displacement of the rigid top layer more evident.
• zwitterionic 150K.mp4: the last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2c; • zwitterionic 300K.mp4: the last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2d; • charge-free 150K.mp4: the last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2e; • charge-free 300K.mp4: the last 6 ns of the MD simulation corresponding to the force trace shown in Figure 2f.